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Question

# A string of length 1 m is fixed at one end with a bob of mass 100 g and the string makes (2π) rev s−1 around a vertical axis through a fixed point. The angle of inclination of the string with the vertical is

A
tan1(58)
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B
tan1(35)
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C
cos1(35)
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D
cos1(58)
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Solution

## The correct option is D cos−1(58)FBD of the bob: Tcosθ=mg ... (1) Tsinθ=mrω2 ... (2) From the diagram, radius of circular path r=lsinθ ∴Tsinθ=m(lsinθ)ω2 ⇒T=mlω2 ... (3) ∴cosθ=mgmlω2 (from (1) and (3)) ω=2πf=2π×2π rad/s ⇒θ=cos−1⎛⎝101×(2π×2π)2⎞⎠ ⇒θ=cos−1(58)

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